Historical notes on the fast Fourier transform

Abstract

a+&,, and look a t t h e residuals X,(t) = X ( t ) -6-6t. This is a new function, which has a spectrum. Is this the spectrum we want? In other words, should one heed advice to pick out and throw away linear trends? The point is that there is no such thing as magically taking out linear trends. If one wants the spectrum

Is computing with the finite Fourier transform pure or applied mathematics?

“…Because p(ö)£ = f a~l a> where /,, a E Z/n, is the orthonormal basis defined above, it follows that p(a) is a unitary operator on L 2 (Z/ri) 9 is a group monomorphism. We will now review briefly, and then extend, the material on the finite Fourier transform that we gave in the Introduction.…”

Elementary Number Theory and Rader's FFT

“…Their method works very well when the number of elements is, for example, a power of two. (Cooley and Tukey were not the first people to develop an FFT [2], but they are the modern proposers of the most commonly used FFT.) In 1968, Rader published an article [6] in which he showed that by reorganizing the computations in a different way, you could also make the calculation of the DFT more efficient when the number of elements is prime.…”

Book Review: Correlation theory of stationary and random functions vol. I; Basic results, vol. II, Supplementary notes and references

“…Initially it was thought that the proposal for such an efficient algorithm was new. However, Yaglom states that the idea for such an algorithm has been traced back to Gauss (for a historical discussion see Cooley, Lewis and Welch, [2] as well as Heideman, Johnson and Burns, [6]). Initial insights into spectral estimation are due to Daniell, Bartlett and slightly later Tukey in the 1940s.…”